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Animation 25
Seeing stationarity emerge in closely spaced paths
symmetry-many-slit-paths-phasors-interference.mp4
These are sparse samples decoded from the current MP4, not newly rendered illustrations. They can support checks of the sampled states and labels, but cannot establish continuous motion, timing, transitions, or the absence of problems between samples. Use the full MP4 when judging those properties.
1280 × 720 · 24 fps · 22.5 s · 540 frames · 12 samples
MP4 SHA-256 05a021cdde8ada00ecd1e43d59d990d0be25a7892cc0cced8b7e047303be2a3e
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Chapter context
Section: Wave Propagation and Interference. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
Seeing stationarity emerge in closely spaced paths
Image description
Many paths, their complex sum, and the resulting interference pattern
Before the animation
Chapter lines 1191–1191
We can repeat the same procedure with many more paths. As the path deviates more from a straight, minimum length path, it has a greater first-order change in phase. (This is the common result from calculus that near a function's minimum, there is no change to the value of the function in the first order of the argument.) When the candidate paths are far from the stationary value, their phases vary greatly, effectively cancelling out their contributions to the total sum. On the other hand, the phases of the paths near the stationary path align and dominate the sum. The green line in the tip-to-tail pane of the animation shows the sum of each of these contributions, giving the amplitude at $B$. The resulting intensity on the projection screen is the square of this magnitude.
After the animation
Chapter lines 1199–1199
We can extend this procedure to its limit and include infinitely many screens with infinitely many slits, and recover unobstructed propagation. In the following animation, we start with a plane wave and recover that same wave. This construction, which provides a bridge to Feynman’s path integral formulation of quantum mechanics, has its roots in Huygens’ wavelets from the late 1600s, extended by Fresnel to include interference in the early 1800s.
Generation source
The same-named canonical entrypoint's main() now delegates to generate_symmetry_desktop_wave_bookends.render_canonical_desktop(); its older draw_frame helpers alone do not reproduce the accepted movie. V7 adds a 96-frame intensity-colored wave intro to a 444-frame centered 49-slit body, then concatenates with FFmpeg stream copy. The recorded build reused content/drafts/animations/iterations/symmetry-many-slit-paths-phasors-interference-20260911T150313560139Z-centered-body.mp4, with its .model.json record; running the canonical entrypoint regenerates that body, while the bookends script supports --reuse-middle. Shared geometry imports pass through the old canonical helpers, wave_paths_explainer, and step2_packet_summary_point. All five main V7 implementation/model files are byte-identical to their scripts/iterations/*-20260911T155628136531Z-v7.py snapshots.
Mapping evidence and limits
Canonical validation identifies iterations/symmetry-many-slit-paths-phasors-interference-v7-intensity-in-the-wave.mp4, 540 frames, 24 fps, 22.5 s, 1280 x 720, the exact body input, and middle_decoded_frames_identical=true. The current MP4 SHA-256 matches its recorded video_sha256 (05a021cdde8ada00ecd1e43d59d990d0be25a7892cc0cced8b7e047303be2a3e). notes/worked/desktop-wave-intensity-field.md confirms the canonical entrypoint and V7 implementation.
Source SHA-256 values identify the exact downloadable bytes in this packet. The source mapping and recorded checks explain the likely generation pipeline; they do not prove that these exact source bytes produced the movie. A GitHub link pinned to a commit is provided only when the delivered source bytes exactly match that path at the build's Git HEAD.
- scripts/generate_symmetry_many_slit_paths_phasors_interference.py · GitHub at 974f9de35254
SHA-256 4b8845f4529bdb1c8643be72b3b415cd305bc01ac54cda304bac840529eb2b54 - scripts/generate_symmetry_desktop_wave_bookends.py · GitHub at 974f9de35254
SHA-256 b6ff52349323d0ce825fad7fc091664b3a3c1a4e166ec23eb2ef605316b1c0ba - scripts/generate_symmetry_slit_tip_to_tail.py · GitHub at 974f9de35254
SHA-256 a75b1c5c5d966911d6a031e3d8c8826acefb18dce40b5171590896ce0d1b4d6d - scripts/perforated_tip_to_tail_model.py · GitHub at 974f9de35254
SHA-256 4c1f497fd6b3508bca022da68099561cb8900868511d99510b2a5e6ceff7c4a7 - scripts/corrected_tip_to_tail_model.py · GitHub at 974f9de35254
SHA-256 6f399befabb8d5cbb22f120d00db405a1aafc513287a8a878c755f0be3d834c9 - scripts/generate_symmetry_wave_paths_explainer.py · GitHub at 974f9de35254
SHA-256 aa6b8924891f48279963539ebd9e5134bb18a1e58c112ac5c40f96c09a6eb111 - scripts/generate_symmetry_step2_packet_summary_point.py · GitHub at 974f9de35254
SHA-256 9286e2052586ef1958124f5d77ac0a3228eea6f8d9c738b382bdbe51f9d0eb0a
Existing generator checks (1 reports)
These are existing author-produced generator reports, copied without changes. Their checks were not rerun for this packet and are not independent certification. A report may describe an earlier generation run; inspect its contents before applying its claims to the current movie.
- symmetry-many-slit-paths-phasors-interference-validation.json
SHA-256 ec7c61f355e16478b5afbc1d6e48c69ad556e345eb651e9f855e1446e9a35bd7
Decoded contact sheet
Extraction method: Twelve evenly spaced decoded frame indices, including first and last. Native-resolution JPEGs from the encoded MP4; timestamps read from FFmpeg showinfo. No source rerendering. Frame indices are zero-based. Sparse samples do not establish continuous motion or capture every transition.. Frame indices are zero-based.
Full-size sampled frames
